Integral problem

**wren17** · Jun 13th 2008, 02:08 PM

The velocity v at time t of an object travelling in a straight line is given by v = t - 3. Determine the distance it travels from t = 0 and t = 4.

**mr fantastic** · Jun 13th 2008, 02:21 PM

Originally Posted by wren17

The velocity v at time t of an object travelling in a straight line is given by v = t - 3. Determine the distance it travels from t = 0 and t = 4.

$\frac{dx}{dt} = t - 3 \Rightarrow x = \frac{t^2}{2} - 3t + C$ .

Assume x(0) = 0: $x = \frac{t^2}{2} - 3t$ .

Note: The answer is NOT x(4) - x(0). Why?

Distance travelled = $\frac{9}{2} + \left( \frac{9}{2} - 4\right) = .....$

Draw a graph of x versus t to see this.

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